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The virtual element method (VEM) allows discretization of elasticity andplasticity problems with polygons in 2D and polyhedrals in 3D. The polygons(and polyhedrals) can have an arbitrary number of sides and can be concave orconvex. These features, among others, are attractive for meshing complexgeometries. However, to the author's knowledge axisymmetric virtual elementshave not appeared before in the literature. Hence, in this work a novel firstorder consistent axisymmetric virtual element method is applied to problems ofelasticity and plasticity. The VEM specific implementation details andadjustments needed to solve axisymmetric simulations are presented.Representative benchmark problems including pressure vessels and circularplates are illustrated. Examples also show that problems of nearincompressibility are solved successfully. Consequently, this researchdemonstrates that the axisymmetric VEM formulation successfully solves certainclasses of solid mechanics problems. The work concludes with a discussion ofresults for the current formulation and future research directions.

Axisymmetric Virtual Elements For Problems of Elasticity and Plasticity